Finding optimal (s, S) policies is about as simple as evaluating a single policy
Coauthor(s): Yu-Sheng Zheng.
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In this paper, a new algorithm for computing optimal (s, S) policies is derived based upon a number of new properties of the infinite horizon cost function c(s, S) as well as a new upper bound for optimal order-up-to levels S* and a new lower bound for optimal reorder levels s*. The algorithm is simple and easy to understand. Its computational complexity is only 2.4 times that required to evaluate a (specific) single (s, S) policy. The algorithm applies to both periodic review and continuous review inventory systems.
Source: Operations Research
Zheng, Yu-Sheng, and Awi Federgruen. "Finding optimal (s, S) policies is about as simple as evaluating a single policy." Operations Research 39, no. 4 (1991): 654-665.